If lx+my=1 touches the circle x^(2)+y^(2...

If lx+my=1 touches the circle `x^(2)+y^(2)=a^(2)`, prove that the point (l,m) lies on the circle `x^(2)+y^(2)=a^(-2)`

Verified by Experts

The correct Answer is:

`:.` Locus of (l,m) is `x^(2)+y^(2)=a^(-2)`

Similar Questions

Explore conceptually related problems

The line y=x+a sqrt(2) touches the circle x^(2)+y^(2)=a^(2) at the point

If 2 y+x+3=0 touches the circle 5 x^(2)+5 y^(2)=k then k=

If (x)/(alpha)+(y)/(beta)=1 touches the circle x^(2)+y^(2)=a^(2) then point ((1)/(alpha), (1)/(beta)) lies on

Show that the line 3x-4y=1 touches the circle x^(2)+y^(2)-2x+4y+1=0 .

From any point on the circle x^(2)+y^(2)=a^(2) , tangtnts are drawn to the circle x^(2)+y^(2)=a^(2) sin ^(2) alpha The anglt between them is

If the line l x+m y+n=0 touches the parabola y^2=4a x , prove that ln=a m^2

The centre of a circle passing through the points (0,0),(1,0) and touching the circle x^(2)+y^(2)=9 is

The equation of the normal to the circle x^(2)+y^(2)-2 x-2 y-2=0 is at the point (3,1) on it is

The circle x^(2) + y^(2) -3x-4y + 2=0 cuts the x axis at the points